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Factor:$$6 x^{3}-6 x^{2}-120 x$$...

Question

Factor:$$6 x^{3}-6 x^{2}-120 x$$

Factor: $$6 x^{3}-6 x^{2}-120 x$$



Answers

Factor: $$6 x^{3}-6 x^{2}-120 x$$

All right. Looking at factoring by grouping today. And the first thing we're gonna do is we're gonna take our four terms, throw some parentheses right in the middle. This one is when it's really important to include the sign of the second turn are the third term right there. So that third term, the sign goes with the right side, that's gonna be vital for us as we move forward. Then we're looking at what is the common term here? Okay, so what's the common term of thes to what we've got three exits in a six x squared. The only thing in common They are the two exes. Ah, in both terms. So we're taking out an X squared. What's left execute divided back squared is just the next x squared about it by X squared is just the one. So six times one which will be six. Look at the 2nd 1 What's in common with two and 12 now this one's a little tricky, cause I think Leo, if you'd just say, Oh, it's a two, I'm done. But there's another thing in common. Oddly enough, there's a negative in common, so I can take out a negative two out of both of these. And so I'm gonna actually factor out and negative, too, because what's a negative two divided by negative, too? Well, that's one. So I end up with one x negative 12 divided by a negative, too. Is positive. Six. So if we didn't take out a native to would end up with a negative X minus six, which is not wrong, but it doesn't match. My other parentheses was just what's really important for factor about grouping. So I really work on making sure those match. So in order to make them match, I needed to take out negative, too, Which is why it's also important that I included the negative in this set of parentheses. Otherwise I would have had a negative to take out of both terms. So make sure you're putting that parentheses in between the sign there up that second and third term. So then, from there, we follow our steps off the greatest common factor in this case, we can take out an X plus six. The parentheses is our greatest common factor, so I'm taking out an X plus six out of both of these terms, literally dividing it out once again. Kind of like a UN distribution. X plus six divided by expert six is just one sign up with the next squared. Same thing happening here. I'm left with the next word minus two. So that is factoring by grouping of this outbreak expression.

We need to find the factors off. 66 square minus 40 next minus 12 1st of all, we will divide the whole expression by two. So we're left with three X Square minus seven X minus six. Now we'll split the middle tum into two numbers and be such that the some off a plus B is equal to minus seven. Noted the coefficient of X on the product off a n B is equal to the product off the coefficient of X square and a constant, um, that is minus 18. So the two numbers would be minus nine and two, so we can write three X Square minus nine X Blessed to X minus six. Now we get dicked three ex common from these totems So three X times X minus tree. Now we can take to common from these two domes. So two ex my mystery No, we can dig X minus three common so extra Ministry times three X plus two No de stumps committed and as X minus tree times expressed to divide by three D are required factors

When it comes to doctoring, you can completely use guess and check to see if you factored something correctly. I'm actually going to use something called the box method. For those of you that hate to guess and check, here's a different way to factor these types of problems. You said of a box like You're going to play four, square outside with your friends and you put the first term in the first bucks and the last term in the last box first term last year. But that sign next. You play a little game, you take the first and last term and multiply them so two times negative six equals negative 12 and you're going to go ahead and try to find to number. Stop multiplying in negative 12 and odd. It's negative one. So you have to think of pairs of numbers that multiply 2 12 and look at each parent. Decide which one could add to negative one. Well, three and four of the best candidates, because I could make the four negative, and now you have three times negative for its negative. 12 3 minus four is negative one, So I'm gonna take these two numbers and put them in my box and doesn't matter which order or where. But you want to put an X with, um could oppose there and show you that we haven't changed this at all. We have it to x squared re X minus for excess negative one X and negative six. Your final step is to factor out common factors beach row and column, for example. The top row has a common factor of X. The bottom row has a common factor of negative, too. The first column has a common factor of two x the second column pads, a common factor of three. The highlighted portions are your factors where your final answer is two x plus three times X minus two. This is the box method.

Okay, So you were going to factor this And because we don't have a one as a little girl vision, we're going to multiply this six to our constant. We get 8 36 and we're gonna look at the factors of 36 so that when I multiply them, I get a negative 36. And when I add the more strapped them, I get a negative pot. So effective as of 36 we have to 18. We have three and 12 when we have four and nine. Okay, so we're gonna dio um and negative 904 Ah, minus nine is a negative six. Negative five. Sorry. And we get our negative 36. So we're gonna write this as six X squared plus four. Excellent as nine X minus six. We keep the same constant. So it's factor by grouping. Pull it in a two x from the 1st 2 terms. We left with a three x plus two dr Out a negative three from the last two terms. We're left with a three x plus. Two backed out that three x plus two and we're left with two X minus three. And that would be our answer


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